In the second paragraph of the poem "Mirror" by Sylvia Plath, why has the mirror been compared to a lake?

Crucial to understanding this poem as a whole is realising
that Sylvia Plath is examining ageing through a very interesting medium. By telling the
poem through the persona of the mirror, she allows us to see the woman who comes to the
mirror and despairs over her ever-increasing wrinkles and
crows-feet.

You are completely right in identifying that in
the second stanza, the mirror suddenly describes itself using a metaphor, saying that it
is now "a lake." It is not literally true, it is just using this comparison to describe
how the woman reacts to it and to prepare us for the shocking ending of the poem. Let us
examine this second stanza in detail:

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Now I am a lake. A woman bends over
me,
Searching my reaches for what she really is.
Then she turns to
those liars, the candles or the moon.
I see her back, and reflect it
faithfully.
She rewards me with tears and an agitation of hands.
I
am important to her. She comes and goes.
Each morning it is her face that
replaces the darkness.
In me she has drowned a young girl, and in me an old
woman
Rises toward her day after day, like a terrible
fish.

Describing herself as a
lake allows the metaphor to effectively describe the action of the woman in her
obsession with the mirror and how she spends so much time looking at it, trying to find
who "she really is." As the poem says, the mirror is "important to her." However, as the
last two lines of the poem comment, the mirror is so important to her that effectively
the woman has "drowned a young girl" in the "lake" that the mirror represents, and in
the mirror each day an old woman rises towards her. Thus the poem comments upon the
finality of ageing and its inevitability. The horrid simile that is used to describe
this process, "like a terrible fish," really gives the poem a lot of
impact.

So, the mirror describes itself as a lake to allow
us to think about the ageing process in different ways. In a sense, it is a kind of
extended metaphor that runs throughout the second stanza and prepares us for its
shocking finale.